Thermal stabilization circuit for an optical ring resonator

ABSTRACT

Disclosed is a thermal stabilization circuit including a heater, which is adjacent and thermally coupled to a closed-curve waveguide of an optical ring resonator, and an analog feedback circuit, which includes a fully autonomous analog feedback loop from a drop port of a bus waveguide of the optical ring resonator to the heater. This analog feedback circuit is configured to dynamically control the electrical power provided to the heater and, thereby to dynamically control the thermal output of the heater in order to tune the ring resonance wavelength to the operating laser wavelength. The analog feedback circuit is further configured to be independent of input power, to be power efficient, to have a relatively small footprint, to have a tunable time constant and to facilitate adjustable wavelength locking. Also disclosed is a device (e.g., a ring-based transceiver or the like), which includes multiple optical ring resonators and corresponding thermal stabilization circuits.

BACKGROUND Field of the Invention

The present invention relates to optical devices and, particularly, to athermal stabilization circuit for an optical ring resonator.

Description of Related Art

Optical ring resonators are often employed as filters or modulators.However, depending upon the materials used to form optical ringresonators and specifically due to the intrinsic properties of thosematerials, optical ring resonators can be thermally sensitive. That is,they can exhibit temperature-dependent resonance shifts (TDRS). Whenthis is the case, thermal stabilization circuits including heaters aretypically employed for temperature adjustment and thereby for control ofthe location of the resonance wavelength. Unfortunately, such thermalstabilization circuits are often digital, complex, and consumesignificant chip area.

SUMMARY

Disclosed herein are embodiments of a circuit structure and,particularly, a thermal stabilization circuit. The structure can includea heater adjacent to an optical ring resonator. The structure can alsoinclude an analog feedback circuit. This analog feedback circuit can beconfigured to detect an optical signal at a drop port of the opticalring resonator, to generate a reference voltage signal using the opticalsignal, and to control power provided to a heater based on the opticalsignal and on the reference voltage signal.

More particularly, some embodiments of a circuit structure and,particularly, a thermal stabilization circuit disclosed herein caninclude a heater adjacent to an optical ring resonator and an analogfeedback circuit connected between the optical ring resonator and theheater. Specifically, the analog feedback circuit can include aphotosensor, which can be configured to receive an optical signal from adrop port of the optical ring resonator and to output an analog currentsignal. The analog feedback circuit can further include acurrent-to-voltage converter, which can be configured to receive theanalog current signal and to output an analog voltage signal. The analogfeedback circuit can further include a peak-based reference voltagegenerator, which can be configured to receive the analog voltage signaland to generate a reference voltage signal based the analog voltagesignal. The analog feedback circuit can further include a comparator,which can be configured to receive the analog voltage signal and thereference voltage signal and to output a voltage control signal. Theanalog feedback circuit can further include an integrator, which can beconfigured to receive the voltage control signal and to output anadjusted voltage signal that is proportional to a time integral of thevoltage control signal. The analog feedback circuit can further includea current mirror, which can be configured to receive the adjustedvoltage signal and to control power provided to the heater based on theadjusted voltage signal.

Also disclosed herein are embodiments of a device structure thatincorporates multiple optical ring resonators and corresponding thermalstabilizations circuits, as described above. That is, a device structuredisclosed herein can include multiple optical ring resonators andthermal stabilization circuits for the optical ring resonators. Eachthermal stabilization circuit for each optical ring resonator caninclude a heater adjacent to the optical ring resonator and an analogfeedback circuit, which can be configured to detect an optical signal ata drop port of the optical ring resonator, to generate a referencevoltage signal using the optical signal, and to control power providedto the heater based on the optical signal and on the reference voltagesignal.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The present invention will be better understood from the followingdetailed description with reference to the drawings, which are notnecessarily drawn to scale and in which:

FIG. 1 is a schematic diagram illustrating disclosed embodiments of athermal stabilization circuit including a heater and an analog feedbackcircuit;

FIG. 2A is a graph illustrating an optical ring resonator through portand drop port transmission-to-wavelength characterization curves;

FIGS. 2B and 2C are graphs illustrating temperature dependence of thedrop port transmission-to-wavelength characterization curve;

FIGS. 3A and 3B are schematic diagrams illustrating different I-to-Vconverters and, particularly, different transimpedance amplifiers (TIAs)that can be incorporated into the analog feedback circuit;

FIG. 4 is a schematic diagram illustrating an exemplary peak-basedreference voltage generator that can be incorporated into the analogfeedback circuit;

FIG. 5 is a schematic diagram illustrating an exemplary Vrefinitialization and reset device that can be incorporated into the analogfeedback circuit;

FIG. 6 is a schematic diagram illustrating an exemplary comparator thatcan be incorporated into the analog feedback circuit;

FIG. 7 is a schematic diagram illustrating an exemplary integrator thatcan be incorporated into the analog feedback circuit;

FIG. 8 is a schematic diagram illustrating an exemplary current mirrorthat can be incorporated into the analog feedback circuit;

FIGS. 9 and 10 are drop port transmission-to-wavelength characterizationcurves illustrating the use of a reference voltage offset amount foroptical modulation amplitude (OMA) optimization; and

FIG. 11 is a schematic diagram illustrating a device that includesmultiple optical ring resonators with thermal stabilization circuits.

DETAILED DESCRIPTION

As mentioned above, an optical ring resonator can exhibit a TDRS,depending upon the materials used to form the optical ring resonator andspecifically due to the intrinsic properties of those materials. Forexample, an optical ring resonator including silicon waveguide corematerial and silicon dioxide waveguide cladding material can exhibitTDRSs of approximately 70 picometers per Kelvin (pm/K) or more. Whenthis is the case, thermal stabilization circuits including heaters aretypically employed for temperature adjustment and thereby for control ofthe location of the resonance wavelength. Unfortunately, such thermalstabilization circuits are often digital, complex, and consumesignificant chip area.

In view of the foregoing, disclosed herein are embodiments of a circuitstructure and, particularly, a thermal stabilization circuit for anoptical ring resonator. The thermal stabilization circuit can include aheater, which is adjacent and thermally coupled to a closed-curvewaveguide of the optical ring resonator. The thermal stabilizationcircuit can further include analog feedback circuit. The analog feedbackcircuit can include a fully autonomous analog feedback loop from a dropport of a bus waveguide of the optical ring resonator to the heater.This analog feedback circuit can be configured to dynamically controlthe power provided to the heater and, thereby to dynamically control thethermal output of the heater in order to tune the ring resonancewavelength to the operating laser wavelength. In the disclosedembodiments, the analog feedback circuit can specifically be configuredso as to be independent of input power, so as to be power efficient, soas to have a relatively small footprint, so as to have a tunable timeconstant and, finally, so as to facilitate adjustable wavelengthlocking. Also disclosed herein are embodiments of a device (e.g., aring-based transceiver or the like), which can include multiple opticalring resonators and corresponding thermal stabilization circuits, asdescribed above.

More particularly, FIG. 1 is a schematic diagram illustrating disclosedembodiments of a circuit structure and, particularly, a thermalstabilization circuit 100 for an optical ring resonator 110.

The optical ring resonator 110 can be, for example, an add-dropmicro-ring resonator configured for multiplexing and/or demultiplexingof wavelengths. Specifically, the optical ring resonator 110 can includemultiple optical waveguides. These waveguides can have silicon cores,silicon nitride cores, or cores of any other suitable waveguide corematerial. The ring waveguides built of silicon core are especiallysensitive for temperature change (effective index of depends on thetemperature). In any case, the optical waveguides of the optical ringresonator 110 can include a first bus waveguide 111 (i.e., an opticalwaveguide with discrete ends) including an input port 116 at one end anda through port 117 at the opposite end. The optical ring resonator 110can further include a second bus waveguide 113 (i.e., another opticalwaveguide with discrete ends) including an optional add port 118 at oneend and a drop port 119 at the opposite end. The optical ring resonator110 can further include a closed-curve waveguide 112 (i.e., an opticalwaveguide with a complete loop or ring shape having no discrete ends),which is spatially separated from but optically coupled to the first andsecond bus waveguides 111 and 113.

In the optical ring resonator 110, an optical signal received at theinput port 116 of the first bus waveguide 111 can include light beams ofone, two, or more wavelengths (e.g., λ1, λ2, etc.) and light beams ofone of those wavelengths (e.g., λ1 only) can interact with the ringresonator (i.e., light beams of all other wavelengths are irrelevant).When the ring resonance wavelength coincide with operating laserwavelength (e.g. λ1 only)—ring operates at the resonance—can beseparated out such that light beams of all wavelengths except λ1 exitthrough the through port 117 and so that light beams of predominately λ1exit out the drop port 119 (as illustrated in the graph of FIG. 2Aincluding curves 201 and 202 representing transmission power (dB) towavelength (λ) at the through port 117 and the drop port 119,respectively). More specifically, the optical ring resonator 110 can beconfigured so that the drop port functions as an alternative output forlight beams confined within the closed-curve waveguide 112 (i.e., forlight beams having the specific resonance wavelength of the closed-curvewaveguide 112). In other words, of all the light beams received at theinput port 116 and passing from the first bus waveguide 111 into theclosed-curve waveguide 112, those light beams that have the specificresonant wavelength for that closed-curve waveguide 112 will makerepeated roundtrips through the closed-curve waveguide 112, building upintensity, due, for example, to constructive interference. Thus, thelight beams that have the specific resonant wavelength and that passfrom the closed-curve waveguide 112 into the second bus waveguide 113and, thereby out the drop port 119 will, predominantly, have thatspecific resonant wavelength. Ideally, the specific resonant wavelengthof the closed-curve waveguide 112 would remain constant at some desiredwavelength (e.g., λ1) such that the light beams at the drop port 119 arepredominately light beams with λ1.

The specific resonant wavelength of a closed-curve waveguide 112 can bethermally sensitive. That is, it can exhibit temperature-dependentresonance shifts (TDRS) so that, depending upon the temperature of theclosed-curve waveguide 112, light beams at the drop port 119 maypredominantly have a wavelength that is either somewhat longer orsomewhat shorter than λ1. For example, if the closed-curve waveguide 112has a silicon core, then the potential TDRS can be, for example,approximately 70 picometers per Kelvin (pm/K) so that the peakwavelength at the drop port is λ1+/− depending upon the direction of theshift. For purposes of this disclosure, the peak wavelength refers tothe wavelength of those light beams that are within the optical signalat the drop port 119 and that have the highest transmission power (dB)(i.e., the wavelength at the peak of the curve 202 in FIG. 2A).

Therefore, disclosed herein are embodiments of a thermal stabilizationcircuit 100 that is configured to compensate for TDRS up or down. Thatis, in the event of TDRS that increases the resonant wavelength of theclosed-curve waveguide 112, the thermal stabilization circuit 100 cancause the thermal output of the heater 115 to decrease, therebydecreasing the temperature of the closed-curve waveguide 112 such thatthe resonant wavelength of the closed-curve waveguide 112 decreasescausing the peak wavelength of the optical signal at the drop port 119to shift downward (e.g., down to λ1) (as illustrated in FIG. 2B).Contrarily, in the event of TDRS that decreases the resonant wavelengthof the closed-curve waveguide 112, the thermal stabilization circuit 100can cause the thermal output of the heater 115 to increase, therebyincreasing the temperature of the closed-curve waveguide 112 such thatthe resonant wavelength of the closed-curve waveguide 112 increasescausing the peak wavelength of the optical signal at the drop port 119to shift upward (e.g., up to λ1) (as illustrated in FIG. 2C). In theevent that no TDRS occurs, the thermal output of the heater 115 willremain unchanged.

The thermal stabilization circuit 100 can include a heater 115 (alsoreferred to herein as a heating element). The heater 115 can be adjacentand thermally coupled to the closed-curve waveguide 112 for thermaltuning. Such a “heater” or “heating element” can be a resistor made ofany suitable conductive material through which electric current can flowand be converted into heat energy. Those skilled in the art willrecognize that the thermal output of the heater and, particularly, theamount of heat generated per unit length will depend upon the level ofpower provided to the heater (e.g., which can create a voltagedifferential across the heating element to cause the electric current toflow and which can be increased or decreased to increase or decrease,respectively, the thermal output of the heater), upon the material used,and on the current density (which is a function of the cross-sectionalarea of the heating element). Various different heater configurationsfor use with optical ring resonators and known in the art and could beincorporated into the thermal stabilization circuit 100. In any case,the heater 115 can be adjacent (e.g., above, below, encircled by orotherwise adjacent to) and thermally coupled to the closed-curvewaveguide 112, as discussed above, so that heat energy from the heater115 can pass to and adjust (up or down) the temperature of theclosed-curve waveguide 112 in order to thermally tune the ring resonantwavelength of the closed-curve waveguide 112 (i.e., in order to achievethe desired resonant wavelength).

The thermal stabilization circuit 100 can further include an analogfeedback circuit 120, which is electrically connected to the heater 115.Generally, this analog feedback circuit 120 can be configured to detectthe optical signal at the drop port 119, to generate a reference voltage(Vref) signal using the optical signal (and, particularly, based on thedetected peak wavelength of the optical signal) and to control the levelof the power provided to the heater 115 based on the optical signal andon the Vref signal. When the power delivered to the heater decreases,the thermal output of the heater 115 decreases, thereby decreasing thetemperature of the closed-curve waveguide 112 such that the resonantwavelength of the closed-curve waveguide 112 decreases causing the peakwavelength of the optical signal at the drop port 119 to shift downward(e.g., down to λ1) (as illustrated in FIG. 2B). When the power deliveredto the heater increases, the thermal output of the heater 115 increases,thereby increasing the temperature of the closed-curve waveguide 112such that the resonant wavelength of the closed-curve waveguide 112increases causing the peak wavelength of the optical signal at the dropport 119 to shift upward (e.g., up to λ1) (as illustrated in FIG. 2C).

The analog feedback circuit 120 can include a photosensor 130. Thephotosensor 130 can be optically coupled to the drop port 119 of thesecond bus waveguide 113 of the optical ring resonator 110. Thephotosensor 130 can receive (e.g., can be configured to receive, can beadapted to receive, etc.) the optical signal 114 (light beams) from thedrop port 119. The photosensor 130 can convert (e.g., can be configuredto convert, can be adapted to convert, etc.) light energy of the opticalsignal 114 into an electrical signal and, particularly, an analogcurrent signal 131. Those skilled in the art will recognize that theelectrical conductance of such a photosensor will vary depending uponthe intensity of the radiation receive including based on the peakwavelength of the optical signal. The photosensor 130 can be, forexample, a photodiode (e.g., a germanium photodiode or some othersuitable type of photodiode). Alternatively, the photosensor 130 can beany other suitable type of photosensor (e.g., a bipolar phototransistor,a photosensitive field effect transistor, etc.).

The analog feedback circuit 120 can further include various additionalcomponents including, but not limited to, a current-to-voltage (I-to-V)converter 140, a peak-based reference voltage (Vref) generator 180, aVref initialization and reset device 190, a comparator 150, anintegrator 160, and a current mirror 170, as discussed in greater detailbelow. FIGS. 3A-3B, 4, 5, 6, 7 and 8 are schematic diagrams illustratingexemplary configurations for these components 140, 180, 190, 150, 160and 170, respectively.

The I-to-V converter 140 can receive (e.g., can be configured toreceive, can be adapted to receive, etc.) the analog current signal 131from the photosensor 130, which is typically at a low level, and canconvert (e.g., can be configured to convert, can be adapted to convert,etc.) that analog current signal 131 to an analog voltage signal 141.FIGS. 3A and 3B are schematic diagrams illustrating two differentexemplary I-to-V converters 140 that could be incorporated into theanalog feedback circuit 120. Specifically, as illustrated in FIG. 3A,the I-to-V converter 140 can be a transimpedance amplifier (TIA) circuitimplemented with an operational amplifier 142 and a feedback resistor143. The operational amplifier 142 can have an inverting input (−)connected to the photosensor 130 for receiving a low-level analogcurrent signal 131, can have a non-inverting input (+) connected toground, and can have an output node 301 for outputting the analogvoltage signal 141. The output node 301 can further be connected by afeedback resistor 143 back to the inverting input (−), which sets thegain of the operational amplifier 142. Alternatively, any other suitableI-to-V converter could be incorporated into the analog feedback circuit120 (e.g., such as the TIA shown in FIG. 3B that employs an inverter 144in place of the operational amplifier shown in FIG. 3A). In any case,the analog voltage signal 141 output by the I-to-V converter 140 can bereceived by both the peak-based reference voltage (Vref) generator 180and the comparator 150, as discussed below.

The peak-based reference voltage generator 180 can receive (e.g., can beconfigured to receive, can be adapted to receive, etc.) the analogvoltage signal 141 and can generate (e.g., can be configured togenerate, can be adapted to generate, etc.) a reference voltage (Vref)signal 181 based the analog voltage signal 141 and on an offset amountfrom a drop port transmission peak, as discussed below. FIG. 4 is aschematic diagram illustrating an exemplary peak-based reference voltagegenerator 180 that can be incorporated into the analog feedback circuit120. Specifically, as illustrated in FIG. 4 , the peak-based referencevoltage generator 180 can include a diode 184 having a diode input and adiode output. The peak-based reference voltage generator 180 can furtherinclude a first amplifier 182 and a second amplifier 187. The firstamplifier 182 can include two first amplifier inputs (i.e., a firstinverting input (−) and a first non-inverting input (+)) and a firstamplifier output. The first amplifier output is connected to the diodeinput, the first non-inverting input is connected to the I-to-Vconverter 140 for receiving the analog voltage signal 141, and the firstinverting input is connected to the diode output. The second amplifier187 includes two second amplifier inputs (i.e., a second inverting input(−) and a second non-inverting input (+)) and a second amplifier output402. The second non-inverting input is connected to the diode output andthe second inverting input is connect to the second amplifier output.The peak-based reference voltage generator 180 can further include acapacitor 186 having conductive plates connected to an intermediate node185, which is between the diode 184 and the second amplifier 187, and toground, respectively. The peak-based reference voltage generator 180 canfurther include an output node 401. A voltage divider 188 can beconnected to the second amplifier output 402 and the output node 401 andcan be configured to output the Vref signal 181 at the output node 401.The voltage divider 188 can include a pair of resistors 189(1)-189(2).These resistors can include a programmable resistor (also referred toherein as a variable resistor) 189(1) connected in series between thesecond amplifier output 402 and the output node 401 and an additionalresistor 189(2) connected between the output node 401 and ground.

Within this peak-based reference voltage generator 180, the connectionsbetween the first amplifier 182 and the diode 184 effectively createwhat is known in the art as a super diode 183. In this super diode, whenthe analog voltage signal 141 at the first non-inverting input (+) ishigher than the diode output voltage at the first inverting input (−),then the first amplifier output will be positive and the diode 184 willbe conductive; whereas when the analog voltage signal 141 at the firstnon-inverting input (−) is lower than the diode output voltage at thefirst inverting input (−), then the first amplifier output will benegative and then the diode 184 will be non-conductive. When the diode184 is conductive, the maximum voltage level of the diode output voltageis effectively tracked and stored in the capacitor 186 and is indicativeof the drop port transmission peak (i.e., of the peak transmission powerof the optical signal at the drop port 119, as illustrated in FIG. 9 ).In the second amplifier 187, when the diode output at the secondnon-inverting input (+) is higher than the second amplifier output atthe second inverting input (−), then the second amplifier output will bepositive; whereas when the diode output at the second non-invertinginput (+) is lower than the second amplifier output at the secondinverting input (−), then the second amplifier output will be negative.Thus, the second amplifier 187 prevents leakage (i.e., discharge of thecapacitor). The voltage divider 188 is programmed to set the Vref signal181 at the output node 401 at a predetermined fraction of the maximumvoltage level (stored in the capacitor 186) given a desired offsetamount from the drop port transmission peak. This offset amount and,thus, the resulting Vref signal 181 are selected to optimize the opticalmodulation amplitude (OMA) of the optical ring resonator 110 (e.g., asshown in FIG. 10 ). Alternatively, any other suitable peak-based Vrefgenerator could be incorporated into the analog feedback circuit 120.

It should be noted that establishment of the offset is discussed ingreater detail below with regard to the Vref initialization and resetdevice 190 (e.g., as shown in FIG. 5 ).

The comparator 150 can receive (e.g., can be configured to receive, canbe adapted to receive, etc.) a pair of inputs specifically during anoperational mode (as opposed to during a reset mode, as discussed indiscussed in greater detail below with regard to the Vref initializationand reset device 190). The inputs can include the analog voltage signal141 from the I-to-V converter 140 and the Vref signal 181 from thepeak-based reference voltage generator 180, via the Vref initializationand reset device 190. The comparator 150 can further output (e.g., canbe configured to output, can be adapted to output, etc.) a voltagecontrol signal 151 given the two inputs. FIG. 6 is a schematic diagramillustrating an exemplary comparator 150 that can be incorporated intothe analog feedback circuit 120. As illustrated, the comparator 150 canbe an operational amplifier 152 with a non-inverting input (+) forreceiving the Vref signal 181, an inverting input (−) for receiving theanalog voltage signal 141, and an output for outputting the voltagecontrol signal 151. In this comparator 150, when the Vref signal 181 atthe non-inverting input (+) is higher than the analog voltage signal 141at the inverting input (−) (indicating that the wavelength of theoptical signal at the drop port 119 needs to be shifted upward), thenthe voltage control signal 151 will be positive. When the Vref signal181 at the non-inverting input (+) is lower than the analog voltagesignal 141 at the inverting input (−) (indicating that the wavelength ofthe optical signal at the drop port 119 needs to be shifted downward),then the voltage control signal 151 will be negative. When the Vrefsignal 181 at the non-inverting input (+) is the same as the analogvoltage signal 141 at the inverting input (−) (indicating that thewavelength of the optical signal at the drop port 119 is at the desiredposition), then the voltage control signal 151 will be 0. Alternatively,any other suitable comparator could be incorporated into the analogfeedback circuit 120. In any case, the voltage control signal 151 outputby the comparator 150 can be received by the integrator 160.

The integrator 160 can receive (e.g., can be configured to receive, canbe adapted to receive, etc.) the voltage control signal 151 from thecomparator 150. Additionally, the integrator 160 can output (e.g., canbe configured to output, can be adapted to output etc.) an adjustedvoltage signal 161, which is proportional to a time integral of thevoltage control signal 151. FIG. 7 is a schematic diagram illustratingan exemplary integrator 160 that can be incorporated into the analogfeedback circuit 120. As illustrated, the integrator 160 can beimplemented using another operational amplifier 162 with a non-invertinginput (+), an inverting input (−) and an output. The integrator 160 canfurther include a pair of resistors 163 and 166, which are connected tothe non-inverting input (+) and inverting input (−) of the operationalamplifier 162, respectively. The voltage control signal 151 can beapplied to the non-inverting input (+) via the resistor 163. Theresistor 166 can be connected between the inverting input (−) of theoperational amplifier 162 and ground. The integrator 160 can furtherinclude a pair of capacitors 164 and 165. The capacitor 164 can beconnected between the non-inverting input (+) of the operationalamplifier 162 and ground. The capacitor 165 can be connected between anoutput node 601 and the inverting input (−) of the operational amplifier162. Optionally, the integrator 160 can further include an integratorreset transistor 167 connected in parallel with the capacitor 165.

With the above-described integrator configuration, when the voltagecontrol signal 151 from the comparator 150 is positive (indicating thatthe wavelength of the optical signal at the drop port 119 needs to beshifted upward), the voltage level of the adjusted voltage signal 161output from the integrator 160 will increase; whereas when the voltagecontrol signal 151 from the comparator 150 is negative (indicating thatthe wavelength of the optical signal at the drop port 119 needs to beshifted downward), the voltage level of the adjusted voltage signal 161output from the integrator 160 will decrease. Alternatively, any othersuitable integrator could be incorporated into the analog feedbackcircuit 120.

It should be noted that the rate of the change to the adjusted voltagesignal 161 output from the integrator 160 will vary depending upon howpositive or how negative the voltage control signal 151 is. For example,when the voltage control signal 151 from the comparator 150 has a highpositive value (indicating that the wavelength of the optical signal atthe drop port 119 needs to be shifted upward by a large amount), thevoltage level of the adjusted voltage signal 161 output from theintegrator 160 can increase relatively fast; whereas, when the voltagecontrol signal 151 from the comparator 150 has a low positive value(indicating that the wavelength of the optical signal at the drop port119 needs to be shifted upward by a small amount), the voltage level ofthe adjusted voltage signal 161 output from the integrator 160 canincrease relatively slowly. Similarly, when the voltage control signal151 from the comparator 150 has a high negative value (indicating thatthe wavelength of the optical signal at the drop port 119 needs to beshifted downward by a large amount), the voltage level of the adjustedvoltage signal 161 output from the integrator 160 can decreaserelatively fast; whereas, when the voltage control signal 151 from thecomparator 150 has a low negative value (indicating that the wavelengthof the optical signal at the drop port 119 needs to be shifted downwardby a small amount), the voltage level of the adjusted voltage signal 161output from the integrator 160 can decrease relatively slowly. Thevarying rate of change of the adjusted voltage signal 161 in response tochanges in the voltage control signal 151 is referred to as the timeconstant for the integrator 160. It should be understood that thevoltage control signal is considered “positive” or “negative” relativeto a common ground in the system (i.e., it is positive if it is higherthan the common ground or negative if it is lower than the commonground) or, alternatively, relative to some arbitrarily selectedvoltage.

The current mirror 170 can receive (e.g., can be configured to receive,can be adapted to receive, etc.) the adjusted voltage signal 161 fromthe comparator 150 and, in response to the adjusted voltage signal 161,can control (e.g., can be configured to control, can be adapted tocontrol, etc.) the level of power (i.e., electrical power) provided tothe heater 115 by adjusting the output current 171 (Iout) that flows tothe heater 115. Specifically, as the adjusted voltage signal 161changes, the output current 171 that flows to the heater 115 and,thereby the level of the power provided to the heater 115 dynamicallychanges (increases or decreases). Furthermore, as the output current 171from the current mirror 170 changes (and thereby the level of powerprovided to the heater 115 changes), the thermal output of the heater115 also changes (e.g., due to corresponding changes in the voltagedifferential across the heating element) in order to control thermaltuning of the optical ring resonator 110. For example, as discussedabove, when the output current 171 that flows to the heater 115decreases (and, thus, the level of power provided to the heater 115decreases), the thermal output of the heater 115 decreases, therebydecreasing the temperature of the closed-curve waveguide 112 such thatthe resonant wavelength of the closed-curve waveguide 112 decreasescausing the peak wavelength of the optical signal at the drop port 119to shift downward (e.g., down to λ1) (as illustrated in FIG. 2B).Conversely, when the output current 171 that flows to the heater 115increases (and, thus, the level of power provided to the heater 115increases), the thermal output of the heater 115 increases, therebyincreasing the temperature of the closed-curve waveguide 112 such thatthe resonant wavelength of the closed-curve waveguide 112 increasescausing the peak wavelength of the optical signal at the drop port 119to shift upward (e.g., up to λ1) (as illustrated in FIG. 2C).

FIG. 8 is a schematic diagram illustrating an exemplary current mirror170 that can be incorporated into the analog feedback circuit 120. Thiscurrent mirror 170 can include two resistors 173 and 175, an n-typefield effect transistor (NFETs) 176 to set a reference current flow, andtwo p-type field effect transistor (PFET) 178 a and 178 b for currentmirroring that depends on the PFETs' area ratio. Specifically, theresistors 173 and 175 can be connected in series between a currentmirror input node and ground. The NFET 176 can be connected in seriesbetween a current mirror node 177 and ground and can further have a gateconnected to an intermediate node 174 at the junction between theresistor 173 and the resistor 175. The PFETs 178 a-178 b can beconnected in parallel with their respective source regions connected toa positive voltage supply rail, with the drain region of the PFET 178 aconnected to the current mirror node 177, with the drain of the PFET 178b connected to a current output node 179, and with their respectivegates connected to the current mirror node 177, as illustrated. Theheater 115 can be connected to the current output node 179 for receivingthe output current (Iout) 171. In operation, the current mirror 170 ofFIG. 8 can receive the adjusted voltage signal 161 at the input node 172and can output Iout 171 at the current output node 179. If the voltagelevel of the adjusted voltage signal 161 increases, the voltage level atthe intermediate node 174 connected to the gate of the NFET 176increases, thereby increasing the conductivity of the NFET 176 andincreasing current flow through the NFET 176 (i.e., increasing Iref).This results in the voltage level at the current mirror node 177decreasing, thereby increasing the conductivity of the PFETs 178 a-178 band causing a corresponding increase in Iout 171. Conversely, if thevoltage level of the adjusted voltage signal 161 decreases, the voltagelevel at the intermediate node 174 connected to the gate of the NFET 176decreases, thereby decreasing the conductivity of the NFET 176 anddecreasing current flow through the NFET 176 (i.e., decreasing Iref).This results in the voltage level at the current mirror node 177increasing, thereby decreasing the conductivity of the PFETs 178 a-178 band causing a corresponding decrease in Iout 171. It should beunderstood that the exemplary current mirror circuit shown in FIG. 8 isprovided for illustration purposes. Alternatively, any other suitablecurrent mirror could be incorporated into the analog feedback circuit120.

It should be noted that, although the thermal output of the heater 115will change as a function of changes in the level of power provided tothe heater 115 (due to changes in the output current 171, as discussedabove), those skilled in the art will recognize that the change in thethermal output will not be instantaneous. Instead the rate of change inthe thermal output of a heater in response to changes in power willdepend upon the heating element materials, dimensions, etc. Furthermore,the rate of the change to the thermal output will vary depending uponhow on the level of change required. For example, if a large change inthe thermal output of the heater is required, the rate of change of thethermal output can be relatively quick; whereas, if only a small changein thermal output is required, the rate of change of the thermal outputcan be relatively slow. The varying rate of change of the thermal outputof the heater 115 in response to changes in the output current 171 isreferred to as the time constant for the heater 115. Therefore, toensure the output current 171 does not change at a rate that is too fastfor the heater 115 to properly respond, the heater 115 and theintegrator 160 can be designed so that they have approximately equaltime constants. That is, they can be designed so that the rate of thechange to the adjusted voltage signal 161 output from the integrator 160in response to changes in the voltage control signal 151 corresponds tothe rate of change of the thermal output of the heater 115 in responseto changes in the output current 171.

As mentioned above, the analog feedback circuit 120 can also include aVref initialization and reset device 190. The Vref initialization andreset device 190 can be connected between the peak-based Vref generator180 and the comparator 150. This device 190 can operation (e.g., can beconfigured to operate, can be adapted to operate, etc.) in either anoperational mode or an initialization/reset mode in response to a modecontrol signal 192 (e.g., from a controller (not shown). The device 190can pass (e.g., can be configured to pass, can be adapted to pass, etc.)the Vref signal 181 from the Vref generator 180 through to thecomparator 150, when operating in the operational mode. The device 190can pass (e.g., can be configured to pass, can be adapted to pass, etc.)a relatively high positive supply voltage signal 191 (e.g., Vdd) to thecomparator 150 (instead of the Vref signal 181), when operating in theinitialization/reset mode. FIG. 5 is a schematic diagram illustrating anexemplary Vref initialization and reset device 190 that can beincorporated into the analog feedback circuit 120. As illustrated, thedevice 190 can include an inverter 193, a transmission gate 195, and apower supply transistor 194. The inverter 193 can receive a mode controlsignal 192 (e.g., from a controller (not shown) and can output aninverted mode control signal 196. The transmission gate 195 can includea PFET and an NFET connected in parallel between an input node and anoutput node. The gate of the PFET can be controlled by the mode controlsignal 192 and the gate of the NFET can be controlled by the invertedmode control signal 196. The power supply transistor 194 can be anadditional PFET, which is connected in series between a positive supplyvoltage rail and the output node. In operation, when the mode controlsignal is low (indicating the operational mode), the inverted modecontrol signal 196 will be high such that the PFET and NFET of thetransmission gate are both on and the power supply transistor 194 isoff. In this case, the Vref signal 181 received at the input node willpass through to the output node and thereby to the comparator 150.However, when the mode control signal is high (indicating theinitialization/reset mode), the inverted mode control signal 196 will below such that the PFET and NFET of the transmission gate are both offand the power supply transistor 194 is on. In this case, the Vref signal181 received at the input node will be prevented from passing through tothe output node (and comparator 150) and instead the output node isconnected to the positive supply voltage rail such that a relativelyhigh positive supply voltage signal 191 passes to the comparator 150.

In the operational mode, the thermal stabilization circuit 100 performsdynamic thermal tuning, as discussed above. Specifically, as describedabove, the thermal stabilization circuit 100 monitors the optical signalat the drop port 119 to detect any change in peak wavelength(corresponding to a TDRS) and, in response to a detected change in thepeak wavelength, adjusts the thermal output of the heater 115 in orderto adjust the temperature of the closed-curve waveguide 112 of theoptical ring resonator 110 and, thereby shift the peak wavelength backup or down as needed (e.g., as illustrated in FIGS. 2B and 2C discussedabove).

In the initialization/reset mode, the full range of power to the heater115 is swept in order to determine the optimal operating position.Specifically, in the initialization/reset mode at circuitinitialization, the comparator 150 can receive a relatively highpositive supply voltage 191 at the non-inverting input (+) and theanalog voltage signal 141 at the inverting input (−). In this case, thehigh positive supply voltage 191 will always be greater than the analogvoltage signal 141, such that the voltage control signal 151 output fromthe comparator 150 is positive in this mode. Thus, the integrator 160will increase the level of the adjusted voltage signal 161, which isproportional to a time integral of the voltage control signal 151 andthe current mirror 170 will increase the output current 171 (Iout) atthe current mirror output node 179 and, thus, increase the level ofpower delivered to the heater 115, thereby increasing the thermal outputof the heater 115 from the minimum heating level to the maximum heatinglevel. During this reset mode (i.e., during the sweep of the heater 115from the minimum heating level to the maximum heating level), theoptical signal at the drop port 119 is sampled in order to determine theoptimal operating position and, more particularly, in order to determinethe optimal offset to use for generating the Vref signal 181. Asdiscussed above, the peak-based Vref generator 180 (e.g., as shown inFIG. 4 ) generates a Vref signal 181 by storing in capacitor 186 chargescorresponding to ring drop-port optical power converted to voltage by aphotosensor130 followed by I-V converter 140. While sweeping heaterpower at least one ring resonance is expected to be found (ring heaterdesign should allow that). Tunable resistor ratio will define a fixedvoltage offset from the maximum (corresponding exactly resonancewavelength) detected 185. The offset can depend on intrinsic ringparameters such as Q-factor or operating voltage and it's needed tomaximize optical modulation amplitude that is defined as lineardifference in the optical between transmitted bit “1” and bit “0”. Inany case, once the optimal offset is determined the voltage divider 188and, particularly, the programmable resistor 189(1) can be programmedaccordingly depending on the type of modulator and peak-to-peak drivingvoltage. Alternatively, any other suitable Vref initialization and resetdevice could be employed to determine the optimal operating position.

It should be noted that upon switching to the operational mode from theinitialization/reset mode (i.e., when the mode control signal 192switches from high to low), the thermal stabilization circuit 100adynamic thermal tuning, as discussed above. Specifically, as describedabove, the Vref signal 181 (which is less than the positive supplyvoltage) will be provided as an input to comparator 150. At the end ofthe initialization/reset mode, the optical signal 114 at the drop port119 will have been generated when the heater 115 was set at the maximumheating level (i.e., at maximum thermal output) and, thus, will have apeak wavelength that in all likelihood needs to be shifted downward by asignificant amount to achieve the desired peak wavelength (e.g., λ1).That is, at the comparator 150 (e.g., see FIG. 6 and the discussionabove), the Vref signal 181 will be less than the analog voltage signal141 such that the voltage control signal 151 is negative. Then, at theintegrator 160 (e.g., see FIG. 7 and the discussion above), a voltagecontrol signal 151 that is negative (indicating that the wavelength ofthe optical signal 114 at the drop port 119 needs to be shifteddownward) results in a decreasing adjusted voltage signal 161 (and,particularly, an adjusted voltage signal proportional to a time integralof the voltage control signal). At the current mirror 170 (e.g., seeFIG. 8 and the discussion above), the decreasing adjusted voltage signal161 results in a decrease in the output current 171 at the currentmirror output node 179 and, thus, a decrease in the level of power beingsupplied to the heater 115 in order to effectively cool the closed-curvewaveguide 112 of the optical ring resonator and, thereby shift the peakwavelength at the drop port 119 downward (shorten wavelength).

The above-described analog feedback circuit 120 is specificallyconfigured so as to be independent of input power, so as to be powerefficient, so as to have a relatively small footprint, so as to have atunable time constant and, finally, so as to facilitate adjustablewavelength locking.

Referring to FIG. 11 , also disclosed herein are embodiments of a device1100 that includes multiple optical ring resonators 110. Each opticalring resonator 110 in the device 1100 can be configured essentially thesame as the optical ring resonator in the above-described structures.That is, each optical ring resonator 110 in the device 1100 can includea closed-curve waveguide 112 positioned laterally between a first buswaveguide 111 and a second bus waveguide 113. Optionally, in someembodiments, two or more of the optical ring resonators 110 in thedevice 1100 can share a common bus waveguide. That is, two or more ofthe optical ring resonators 110 can have a closed-curved waveguide 112that is positioned laterally between a corresponding portion of a sharedfirst bus waveguide 111 and a discrete second bus waveguide 113.

The device 1100 can further include thermal stabilization circuits 100,also as described above, for at least some of the optical ringresonators 110. Each thermal stabilization circuit 100 for a given oneof the optical ring resonators 110 can include a heater 115 adjacent tothe closed-curve waveguide 112 of that optical ring resonator 110.Additionally, each thermal stabilization circuit 100 for a given one ofthe optical ring resonators 110 can include an analog feedback circuit120, which can detect an optical signal 114 at a drop port 119 of thatoptical ring resonator 110, which can generate a reference voltage(Vref) signal 181 using the optical signal 114, and which can controlpower provided to the heater 115 based on the optical signal 114 and onthe Vref signal 181 in the same manner as described in detail above withregard to FIG. 1 . It should be noted that such a device 1100 could beany optoelectronic device that includes multiple optical ringresonators.

For example, the device 1100 could be a ring-based transceiver, asillustrated in FIG. 11 . The ring-based transceiver can, for example, bea wavelength-division multiplexing (WDM) optical transceiver. Thistransceiver can include a transmitter section 1110 and a receiversection 1120. The transmitter section 1110 can include, for example, aring modulator bank with multiple optical ring resonators 110. Eachoptical ring resonator 110 in the bank in the transmitter section 1110can have a different resonant wavelength (e.g., λ1-λ4) and can beconnected to a corresponding thermal stabilization circuit 100(including a heater 115 and analog feedback circuit 120, as describedabove) configured to maintain that resonant wavelength. The receiversection 1120 can include, for example, a ring filter bank with multipleoptical ring resonators 110. Each optical ring resonator 110 in the bankin the receiver section 1120 can have a different resonant wavelength(e.g., λ1-λ4) and can be connected to a corresponding thermalstabilization circuit 100 (including a heater 115 and analog feedbackcircuit 120). It should be understood that the thermal stabilizationscircuits 100 in the transmitter section 1110 and the receiver section1120 would be very similarly designed but specifically configured tomaintain the resonant wavelengths of the respective sections.Alternatively, the device could be any other type of device thatincludes multiple optical ring resonators requiring thermalstabilization (e.g., a ring-based transmitter, a ring-based receiver,etc.).

It should be understood that the terminology used herein is for thepurpose of describing the disclosed structures and methods and is notintended to be limiting. For example, as used herein, the singular forms“a”, “an” and “the” are intended to include the plural forms as well,unless the context clearly indicates otherwise. Additionally, as usedherein, the terms “comprises” “comprising”, “includes” and/or“including” specify the presence of stated features, integers, steps,operations, elements, and/or components, but do not preclude thepresence or addition of one or more other features, integers, steps,operations, elements, components, and/or groups thereof. Furthermore, asused herein, terms such as “right”, “left”, “vertical”, “horizontal”,“top”, “bottom”, “upper”, “lower”, “under”, “below”, “underlying”,“over”, “overlying”, “parallel”, “perpendicular”, etc., are intended todescribe relative locations as they are oriented and illustrated in thedrawings (unless otherwise indicated) and terms such as “touching”, “indirect contact”, “abutting”, “directly adjacent to”, “immediatelyadjacent to”, etc., are intended to indicate that at least one elementphysically contacts another element (without other elements separatingthe described elements). The term “laterally” is used herein to describethe relative locations of elements and, more particularly, to indicatethat an element is positioned to the side of another element as opposedto above or below the other element, as those elements are oriented andillustrated in the drawings. For example, an element that is positionedlaterally adjacent to another element will be beside the other element,an element that is positioned laterally immediately adjacent to anotherelement will be directly beside the other element, and an element thatlaterally surrounds another element will be adjacent to and border theouter sidewalls of the other element. The corresponding structures,materials, acts, and equivalents of all means or step plus functionelements in the claims below are intended to include any structure,material, or act for performing the function in combination with otherclaimed elements as specifically claimed.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

What is claimed is:
 1. A structure comprising: a heater adjacent to an optical ring resonator; and an analog feedback circuit configured to detect an optical signal at a drop port of the optical ring resonator, to generate a reference voltage signal using the optical signal, and further to control power provided to a heater based on the optical signal and on the reference voltage signal.
 2. The structure of claim 1, wherein the optical ring resonator comprises: a first bus waveguide having an input port and a through port; a second bus waveguide having the drop port; and a closed-curve waveguide between the first bus waveguide and the second bus waveguide, wherein the heater is adjacent to the closed-curve waveguide and wherein the power controls a thermal output of the heater so as to tune a ring resonance wavelength.
 3. The structure of claim 1, wherein the analog feedback circuit comprises: a photosensor configured to receive the optical signal from the drop port and to output an analog current signal; a current-to-voltage converter configured to receive the analog current signal and to output an analog voltage signal; and a peak-based reference voltage generator configured to receive the analog voltage signal and to generate the reference voltage signal based the analog voltage signal.
 4. The structure of claim 3, wherein the peak-based reference voltage generator further generates the reference voltage signal based on an offset amount from a drop port transmission peak.
 5. The structure of claim 4, wherein the peak-based reference voltage generator comprises: a diode having a diode input and a diode output; a first amplifier comprising: two first amplifier inputs and a first amplifier output, wherein the first amplifier output is connected to the diode input and wherein the two first amplifier inputs are connected to the current-to-voltage converter for receiving the analog voltage signal and to the diode output, respectively; a second amplifier comprising two second amplifier inputs and a second amplifier output, wherein the two second amplifier inputs are connected to the diode output and to the second amplifier output, respectively; a capacitor connected to an intermediate node between the diode and the second amplifier and to ground and configured to store a maximum voltage level corresponding to the drop port transmission peak; an output node; and a voltage divider connected to the second amplifier output and the output node, wherein the voltage divider is configured to output the reference voltage signal at the output node such that the reference voltage signal is a predetermined fraction of the maximum voltage level given the offset amount.
 6. The structure of claim 5, wherein the voltage divider comprises: a programmable resistor connected in series between the second amplifier output and the output node; and an additional resistor connected between the output node and ground.
 7. The structure of claim 3, wherein the analog feedback circuit further comprises: a comparator configured to receive the analog voltage signal and the reference voltage signal and to output a voltage control signal; an integrator configured to receive the voltage control signal and to output an adjusted voltage signal proportional to a time integral of the voltage control signal; and a current mirror configured to receive the adjusted voltage signal and to control the power provided to the heater.
 8. The structure of claim 7, wherein the heater and the integrator have approximately equal time constants.
 9. The structure of claim 7, wherein the analog feedback circuit further comprises: a reset device connected between the peak-based reference voltage generator and the comparator, wherein the reset device is operable in one of an operational mode and a reset mode in response to a mode control signal, wherein in the operational mode the reset device passes the reference voltage signal to the comparator, and wherein in the reset mode the reset device passes a positive supply voltage signal to the comparator.
 10. A structure comprising: a heater adjacent to an optical ring resonator; and an analog feedback circuit comprising: a photosensor configured to receive an optical signal from a drop port of the optical ring resonator and to output an analog current signal; a current-to-voltage converter configured to receive the analog current signal and to output an analog voltage signal; a peak-based reference voltage generator configured to receive the analog voltage signal and to generate a reference voltage signal based the analog voltage signal; a comparator configured to receive the analog voltage signal and the reference voltage signal and to output a voltage control signal; an integrator configured to receive the voltage control signal and to output an adjusted voltage signal proportional to a time integral of the voltage control signal; and a current mirror configured to receive the adjusted voltage signal and to control power provided to the heater.
 11. The structure of claim 10, wherein the optical ring resonator comprises: a first bus waveguide having an input port and a through port; a second bus waveguide having the drop port; and a closed-curve waveguide between the first bus waveguide and the second bus waveguide, wherein the heater is adjacent to the closed-curve waveguide and wherein the power controls a thermal output of the heater so as to tune a resonance wavelength.
 12. The structure of claim 10, wherein the peak-based reference voltage generator further generates the reference voltage signal based on an offset amount from a drop port transmission peak.
 13. The structure of claim 12, wherein the peak-based reference voltage generator comprises: a diode having a diode input and a diode output; a first amplifier comprising: two first amplifier inputs and a first amplifier output, wherein the first amplifier output is connected to the diode input and wherein the two first amplifier inputs are connected to the current-to-voltage converter for receiving the analog voltage signal and to the diode output, respectively; a second amplifier comprising two second amplifier inputs and a second amplifier output, wherein the two second amplifier inputs are connected to the diode output and to the second amplifier output, respectively; a capacitor connected to an intermediate node between the diode and the second amplifier and to ground and configured to store a maximum voltage level corresponding to the drop port transmission peak; an output node; and a voltage divider connected to the second amplifier output and the output node, wherein the voltage divider is configured to output the reference voltage signal at the output node such that the reference voltage signal is a predetermined fraction of the maximum voltage level given the offset amount.
 14. The structure of claim 13, wherein the voltage divider comprises: a programmable resistor connected in series between the second amplifier output and the output node; and an additional resistor connected between the output node and ground.
 15. The structure of claim 10, wherein the heater and the integrator have approximately equal time constants.
 16. The structure of claim 10, wherein the analog feedback circuit further comprises: a reset device connected between the peak-based reference voltage generator and the comparator, wherein the reset device operates in one of an operational mode and a reset mode in response to a mode control signal, wherein in the operational mode the reset device passes the reference voltage signal to the comparator, and wherein in the reset mode the reset device passes a positive supply voltage signal the comparator.
 17. A structure comprising: optical ring resonators; and thermal stabilization circuits for the optical ring resonators, wherein each thermal stabilization circuit for each optical ring resonator comprises: a heater adjacent to the optical ring resonator; and an analog feedback circuit detecting an optical signal at a drop port of the optical ring resonator, generating a reference voltage signal using the optical signal, and further controlling power provided to the heater based on the optical signal and on the reference voltage signal.
 18. The structure of claim 17, wherein each optical ring resonator comprises: a portion of a first bus waveguide, wherein the first bus waveguide has an input port and a through port; a second bus waveguide having the drop port; and a closed-curve waveguide between the first bus waveguide and the second bus waveguide, wherein the heater of the thermal stabilization circuit for each optical ring resonator is adjacent to the closed-curve waveguide of the optical ring resonator, and wherein the power provided to the heater controls a thermal output of the heater so as to tune a resonance wavelength.
 19. The structure of claim 17, wherein the analog feedback circuit of the thermal stabilization circuit for each optical ring resonator comprises: a photosensor configured to receive the optical signal from the drop port and to output an analog current signal; a current-to-voltage converter configured to receive the analog current signal and to output an analog voltage signal; a peak-based reference voltage generator configured to receive the analog voltage signal and to generate the reference voltage signal based the analog voltage signal and on an offset amount from a drop port transmission peak; a comparator configured to receive the analog voltage signal and the reference voltage signal and to output a voltage control signal; an integrator configured to receive the voltage control signal and to output an adjusted voltage signal proportional to a time integral of the voltage control signal, wherein the heater and the integrator have approximately equal time constants; and a current mirror configured to receive the adjusted voltage signal and to output the current output signal to the heater.
 20. The structure of claim 19, wherein the peak-based reference voltage generator of the corresponding analog feedback circuit comprises: a diode having a diode input and a diode output; a first amplifier comprising: two first amplifier inputs and a first amplifier output, wherein the first amplifier output is connected to the diode input and wherein the two first amplifier inputs are connected to the current-to-voltage converter for receiving the analog voltage signal and to the diode output, respectively; a second amplifier comprising two second amplifier inputs and a second amplifier output, wherein the two second amplifier inputs are connected to the diode output and to the second amplifier output, respectively; a capacitor connected to an intermediate node between the diode and the second amplifier and to ground and configured to store a maximum voltage level corresponding to the drop port transmission peak; an output node; and a voltage divider connected to the second amplifier output and the output node, wherein the voltage divider is configured to output the reference voltage signal at the output node such that the reference voltage signal is a predetermined fraction of the maximum voltage level given the offset amount, and wherein the corresponding analog feedback circuit further comprises a reset device connected between the peak-based reference voltage generator and the comparator, wherein the reset device is operable in one of an operational mode and a reset mode in response to a mode control signal, wherein in the operational mode the reset device passes the reference voltage signal to the comparator, and wherein in the reset mode the reset device passes a positive supply voltage signal to the comparator. 